General Relativity and Quantum Cosmology

Title:Global Embedding of the Reissner-Nordström Metric in the Flat Ambient Space

Abstract: We study isometric embeddings of non-extremal Reissner-Nordström metric
describing a charged black hole. We obtain three new embeddings in the flat
ambient space with minimal possible dimension. These embeddings are global,
i.e. corresponding surfaces are smooth at all values of radius, including
horizons. Each of the given embeddings covers one instance of the regions
outside the horizon, one instance between the horizons and one instance inside
the internal horizon. The lines of time for these embeddings turn out to be
more complicated than circles or hyperbolas. The obtained embeddings are also
smooth at all values of radius for extremal and hyperextremal black holes.

Comments:

LaTeX, 12 pages, in this version we stressed that obtained new embeddings are also global and smooth for extremal and hyperextremal black holes